In a nuclear reactor, a fissile fuel atom, such as U-235, absorbs a neutron in its nucleus and undergoes a nuclear disintegration which produces on the average two fission fragments of lower atomic weight with great kinetic energy and several neutrons also at high energy.
In a typical boiling water reactor (BWR), the nuclear fuel is in the form of fuel rods, each of which comprises a plurality of sintered pellets contained within an elongated cladding tube. Groups of such fuel rods are supported between upper and lower tie plates to form separately replaceable fuel assemblies or bundles. A sufficient number of such fuel assemblies are arranged in a matrix, approximating a right circular cylinder, to form the nuclear reactor core which is capable of self-sustained fission reaction. The kinetic energy of the fission products is dissipated as heat in the fuel rods. Energy is also deposited in the fuel structure and moderator by the neutrons, gamma rays, and other radiation resulting from the fission process. The core is submerged in coolant (for example, water) which removes the heat which may then be extracted to perform useful work. Where the coolant is water, it also acts as a neutron moderator, which slows down the neutrons to render them more likely to initiate a fission reaction.
The commonly used fuel for water cooled and moderated nuclear power reactors comprises uranium dioxide of which from about 0.7 to about 5.0 percent is fissile U-235 mixed with fertile U-238. During operation of the reactor, some of the fertile U-238 is converted to fissile Pu-239 and Pu-241. The U-238 also is fissile, but only for high energy neutrons. The ratio of fissile material produced (for example, Pu-239 and Pu-241) to fissile material destroyed (for example, U-235, Pu-239, and Pu-241) is defined to be the "conversion ratio."
If the reactor is to operate at a steady state power level, the fission-inducing neutron population must remain constant. That is, each fission reaction must produce a net of one neutron which produces a subsequent fission reaction so that the operation is self-sustaining. The operation is characterized by an effective multiplication factor k.sub.eff which must be at unity for steady state operation. It is noted that the effective multiplication factor k.sub.eff is the neutron reproduction factor of the nuclear reactor considered as a whole, and is to be distinguished from the local or infinite multiplication factor k.sub.inf which defines the neutron reproduction of an infinitely large system having throughout the same composition and characteristics as the local region of the reactor core in question.
During operation, the fissile fuel is depleted, and indeed, some of the fission products are themselves neutron absorbers or "poisons." To offset this, the reactor is normally provided with an initial excess of nuclear fuel which results in initial excess reactivity. This initial excess reactivity requires a control system to maintain the effective multiplication factor at unity during reactor operations and to reduce the effective multiplication factor to below unity in the event that it is necessary to shut down the reactor. The control system typically utilizes neutron absorbing material which serves to control the neutron population by non-fission absorption or capture of neutrons.
At least a portion of the neutron absorbing material is incorporated in a plurality of selectively actuatable control rods which are axially inserted from the bottom of the core as required to adjust the power level and distribution and to shut down the core. Burnable absorbers may be incorporated into some of the fuel rods to minimize the amount of mechanical control required. A burnable absorber is a neutron absorber which is converted by neutron absorption into a material of lesser neutron absorbing capability. A well-known burnable absorber is gadolinium, normally in the form of gadolinia. The odd isotopes (Gd-155 and Gd-157) have very high capture cross sections for thermal neutrons. The burnable absorbers available for use in design have an undesirable end-of-refueling cycle neutron absorption reactivity residual due to residual isotopic neutron absorption by small neutron cross section absorbers. For example, if gadolinium is used as a burnable absorber, the high cross section isotopes (Gd-155 and Gd-157) deplete rapidly but residual absorption remains due to continued neutron capture in the even isotopes (Gd-154, Gd-156, and Gd-158).
As is well known, burnable absorbers such as gadolinium operate in a self-shielded mode when present at sufficient concentration. That is, upon exposure to the neutron flux, the neutron absorption occurs essentially at the outer surface of the absorber so that the volume of absorber shrinks radially at a rate that depends on the concentration of absorber. It is then possible, by a suitable choice of the number of absorber-containing regions and the absorber concentrations therein, to provide a desired variation of the absorption worth over one or more reactor operating cycles.
During operation, the percentage of steam voids increases towards the top of the reactor, leading to decreased moderation in the top regions, and thus a power distribution that is skewed toward the lower regions of the core. It is a known practice to compensate for this by distributing burnable absorber in an axially inhomogeneous manner. A number of fuel rods are provided with burnable absorber having a distribution skewed toward the axial region of hot operating maximum reactivity. A typical configuration is shown in U.S. Pat. No. 3,799,839.
However, the situation is very different in the cold shutdown state. More particularly, in the cold state, the top of an irradiated BWR core is more reactive than the bottom due to greater plutonium production and less U-235 destruction in the top during operation (greater conversion ratio and smaller burnup in the top of the core). In the cold shutdown condition, the steam voids in the upper part of the core are eliminated, thus making the top of the core more reactive than the bottom. Typical licensing standards require a 0.38% reactivity shutdown margin (k.sub.eff less than 0.9962) with any one control rod stuck out of the core. To provide margin for prediction uncertainties, a design basis of 1% predicted shutdown margin (k.sub.eff less than 0.99), to be provided by the control rods and the burnable absorbers, typically is used.
While axial power shaping may be carried out by providing greater amounts of burnable absorber in the lower portions of the reactor core, the optimum absorber shape for full power axial power shape optimization does not lend itself to maintaining adequate cold shutdown margin. In order to meet cold shutdown constraints, it is typically necessary to design with excess burnable absorber residual which penalizes the initial enrichment and uranium ore requirements and increases the fuel cycle cost of the reactor.
A further problem is that gadolinia reduces the thermal conductivity of the fuel rods and increases fission gas release. Consequently, the gadolinia-containing rods are frequently the most limiting rods in the fuel assembly, and have to be down-rated in power with a correspondingly adverse effect on local power distributions. The amount of power down-rating that is required depends on the gadolinia concentration, but becomes a serious problem in extended burnup fuel bundle designs and/or high energy cycle designs where increased gadolinia concentrations are required in order to provide adequate cold shutdown margins.
Thus, the margins required for the hot operating and cold shutdown conditions place competing constraints on the reactor core design, and have thus tended to prevent the achievement of an optimal core configuration.